(3) Compressed Sensing (CS)
Concept and need for CS
Theoretical treatment: concept of coherence, null-space property and restricted isometry property, proof of a key theorem in CS
Algorithms for CS (covered in part 2) and some key properties of these algorithms
Applications of CS: Rice Single Pixel Camera and its variants, Video compressed sensing, Color and Hyperspectral CS, Applications in Magnetic Resonance Imaging (MRI), Implications for Computed Tomography
CS under Forward Model Perturbations: a few key results and their proofs as well as applications
Designing Forward Models for CS
Low-rank matrix estimation and Robust Principal Components Analysis: concept and application scenarios in image processing, statement of some key theorems, and proof of one important theorem

References

We will extensively refer to the following textbooks, besides a number of research papers from journals such as IEEE Transactions on Image Processing, IEEE Transactions on Signal Processing, and IEEE Transactions on Pattern Analysis and Machine Intelligence: